Over the last thirty years, computer tomography (CT) has gone from image reconstruction based on scanning in a slice-by-slice process to spiral scanning to also include non-spiral scanning techniques such as those performed with C-arm devices, with all techniques and devices experiencing problems with image reconstruction.
From the 1970s to 1980s the slice-by-slice scanning was used. In this mode the incremental motions of the patient on the table through the gantry and the gantry rotations were performed one after another. Since the patient was stationary during the gantry rotations, the trajectory of the x-ray source around the patient was circular. Pre-selected slices through the patient were reconstructed using the data obtained by such circular scans.
From the mid 1980s to present day, spiral type scanning has become the preferred process for data collection in CT. Under spiral scanning a table with the patient continuously moves at a constant speed through the gantry that is continuously rotating about the table. At first, spiral scanning has used one-dimensional detectors, which receive data in one dimension (a single row of detectors). Later, two-dimensional detectors, where multiple rows (two or more rows) of detectors sit next to one another, have been introduced. In CT there have been significant problems for image reconstruction especially for two-dimensional detectors. Data provided by the two-dimensional detectors will be referred to as cone-beam (CB) data or CB projections.
In addition to spiral scans there are non-spiral scans, in which the trajectory of the x-ray source is different from spiral. In medical imaging, non-spiral scans are frequently performed using a C-arm device, which is usually smaller and more portable than spiral type scanning systems. For example, C-arm scanning devices have been useful for being moved in and out of operating rooms, and the like.
FIG. 1 shows a typical prior art arrangement of a patient on a table that moves through a C-arm device, that is capable of rotating around the patient, having an x-ray tube source and a detector array, where cone beam projection data sets are received by the x-ray detector, and an image reconstruction process takes place in a computer with a display for the reconstructed image.
There are known problems with using C-arm devices to reconstruct data. See in particular for example, pages 755-759 of Kudo, Hiroyuki et al., Fast and Stable Cone-Beam Filtered Backprojection Method for Non-planar Orbits, IOP Publishing LTD, 1998, pages 747-760. The Kudo paper describes image reconstruction using C-arm devices for various shift-variant filtered back projection (FBP) structures, which are less efficient than convolution-based FBP algorithms.
For three-dimensional (also known as volumetric) image reconstruction from the data provided by spiral and non-spiral scans with two-dimensional detectors, there are two known groups of algorithms: Exact algorithms and Approximate algorithms, that each have known problems. Under ideal circumstances, exact algorithms can provide a replication of an exact image. Thus, one should expect that exact algorithms would produce images of good quality even under non-ideal (that is, realistic) circumstances.
However, exact algorithms can be known to take many hours to provide an image reconstruction, and can take up great amounts of computer power when being used. These algorithms can require keeping considerable amounts of cone beam projections in memory.
Approximate algorithms possess a filtered back projection (FBP) structure, so they can produce an image very efficiently and using less computing power than Exact algorithms. However, even under the ideal circumstances these algorithms produce an approximate image that may be similar to but still different from the exact image. In particular, Approximate algorithms can create artifacts, which are false features in an image. Under certain circumstances and conditions these artifacts could be quite severe.
To date, there are no known algorithms that can combine the beneficial attributes of Exact and Approximate algorithms into a single algorithm that is capable of replicating an exact image under the ideal circumstances, uses small amounts of computer power, and reconstructs the exact images in an efficient manner (i.e., using the FBP structure) in the cases of complete circle and arc and incomplete circle and arc scanning.
If the C-arm rotates 360 degrees around the patient, this produces a complete circle. If the C-arm rotates less than 360 degrees around the patient, this produces an incomplete circle. In what follows, the word circle covers both complete and incomplete cases. Here and everywhere below by the phrase that the algorithm of the invention reconstructs an exact image we will mean that the algorithm is capable of reconstructing an exact image. Since in real life any data contains noise and other imperfections, no algorithm is capable of reconstructing an exact image.
Image reconstruction has been proposed in many U.S. patents. See for example, U.S. Pat. Nos. 5,663,995 and 5,706,325 and 5,784,481 and 6,014,419 to Hu; U.S. Pat. Nos. 5,881,123 and 5,926,521 and 6,130,930 and 6,233,303 and 6,292,525 to Tam; U.S. Pat. No. 5,960,055 to Samaresekera et al.; U.S. Pat. No. 5,995,580 to Schaller; U.S. Pat. No. 6,009,142 to Sauer; U.S. Pat. No. 6,072,851 to Sivers; U.S. Pat. No. 6,173,032 to Besson; U.S. Pat. No. 6,198,789 to Dafni; U.S. Pat. Nos. 6,215,841 and 6,266,388 to Hsieh. Other U.S. patents have also been proposed for image reconstruction as well. See U.S. Pat. No. 6,504,892 to Ning; U.S. Pat. No. 6,148,056 to Lin; U.S. Pat. No. 5,784,481 to Hu; U.S. Pat. No. 5,706,325 to Hu; U.S. Pat. No. 5,170,439 to Zeng et al.
However, none of the patents overcome all of the deficiencies to image reconstruction referenced above. The inventor is not aware of any known processes, methods and systems that combines the beneficial attributes of Exact and Approximate algorithms into a single algorithm that is capable of replicating an exact image under the ideal circumstances, uses small amounts of computer power, and reconstructs the exact images in an efficient manner (i.e., using the FBP structure) in the cases of complete circle and arc and incomplete circle and arc scanning.